Frequency locking, Quasi periodicity and Chaos due to special relativistic effects

TL;DR

This paper investigates how special relativistic effects influence the dynamics of driven harmonic oscillators, revealing phenomena like frequency locking, quasi-periodicity, chaos, and multistability, with implications for relativistic nonlinear systems.

Contribution

It demonstrates the emergence of complex dynamical behaviors due to relativistic effects in driven oscillators, including frequency locking, chaos, and multistability, extending understanding of relativistic nonlinear dynamics.

Findings

Relativistic effects cause frequency shifts leading to locking and quasi-periodic states.

Chaos is enhanced in the relativistic Henon-Heiles system.

Multistability occurs with small damping in the relativistic oscillator.

Abstract

We study quasi periodic and frequency locked states that can occur in a sinusoidally driven linear harmonic oscillator in the special relativistic regime. We show how the shift in natural frequency of the oscillator with increasing relativistic effects leads to frequency locking or quasi periodicity and the chaotic states that arise due to the increasing non linearity. We find the same system can have multi-stable states in the presence of small damping. We also report an enhancement of chaos in the relativistic Henon-Heiles system.